The Lewis Structure: An Expanded Perspective James L. Reed Clark Atlanta University, Atlanta, GA30314
The Lewis electron dot structure was firiit introduced in 1916 bv Gilbert N.Lewis 11,and has ~nwidedrcmrrations of cheiists with a versatile semiqu~ntitative~description of both bonding and structure. These structures themselves constitute a diagrammatical representation of the electronic structure of a molecule rendered in the valence bond model. However, current bonding theory is dominated by the molecular orbital model. Because beginning students are introduced to both the valence bond and molecular orbital theories, they are often confronted with two seeminelv - " contradictorv descriotions for the same nhenomenon (2). In addition to theories that describe bondine and structure, students also need an introduction to tGeories that rationalize chemical reactivity. Pi-electron theory, Woodward-Hoffman theory, and the frontier-electron theory of Fukui have played key roles in this area (3).However, because their use often requires a detailed knowledge of the molecular orbitals, their usefulness to students is often limited ( 4 , 5 ) . Here we give students a simple bridge between the molecular orbital and valence bond models. We help students enjoy the benefits of frontier and molecular orbital theories without the need for sophisticated and complex computations.
as ione pair electrons. The following equation is the response (Ap(r))of Fz to the removal ( A N = -2) of two electrons.
(3)
Thus, it is a description of the f_or the HOMO. We observe that the presence of these electrons causes a decrease in bonding. Thus, they should be characterized as antibonding. Also, the change in bonding occurs in the pi bond order. Thus, these electrons and the HOMO are pi-antibonding. Furthermore, presence of these electrons causes the electron density in the intranuclear region to decrease (two electrons versus four) and in the outer region to increase (to six lone pairs).
The Frontier Function The frontier or Fukui function f(r) provides a description of the frontier electron density,
where p(r) is the electron density a t position r, and N i s the number of electrons in the molecule. Furthermore, when in the finite difference form,
the highest occupied molecular orbital (HOMO) is described by f_ V(r) for AN < 01, and the lowest unoccupied molecular orbital (LUMO) by f+ R r ) for AN > 0) (6, 7). Because the Lewis structure is a representation of the electronic structure p(r), its response Ap(r) to changes in the number of electrons (AN = f l , +!2) yields a description of the Fukui function and thus the frontier orbitals. Valence Bonds and Molecular Orbitals When students are introduced to both valence bond and molecular orbital theory, they are exposed to two seemingly unrelated theories. For example, the antibonding electrons of molecular orbital theory are seemingly absent from valence bond theory. Such electrons are characterized as yielding a repulsive interaction between the relevant atoms as well as a decrease in electron density in the internuclear region and an increase in the outer regions. Using Changes in Lewis Structures To Study Molecular Orbitals
Acwrding to the molecular orbital model the highest ene r w electrons of fluorine are in antibondine orbitals of oi symmetry, but the Lewis structure seems to describe these
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98
Journal of Chemical Education
The addition of two electrons to fluorine yields a 16-electron system for which the bond must be broken to yield the optimal Lewis structures. Therefore the lowest unoccupied molecular orbital (LUMO and f+) must be sigma-antibonding. The removal of two electrons yields information about the HOMO, whereas the removal of an additional two electrons shows that the next lower energy orbital is also piautibonding. Thus, the description and the order of the three highest energy orbitals are obtainable from the Lewis structures and are identical to those found using molecular orbital methods. These results suggest that the information that is explicit in the molecular orbitals and in Fukui functions can be implicitly found in the Lewis structures. Probing the LUMO and HOMO of Polyatomic Molecules
This methodology need not be limited to simple diatomic molecules. Perhaps one of the more dramatic examples is nitrous oxide (N-N'-0) whose ionizations are depicted a t the top of the next page in eq 5, where these are the optimal Lewis structures. The HOMO or f., which is probed by the the removal of two electrons (AN = -21, is nonbonding because neither the sigma nor pi bond order changes. However, the situation is
